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Question

# The figure shows a circle with centre O and radius 8 cm. ∠ BOD =72∘. The radius of the smaller circle is 4 cm. A point is selected randomly inside the larger circle, find the probability that the point lies neither inside the smaller circle nor inside the sector.

A
1320
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B
35
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C
1120
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D
12
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Solution

## The correct option is C 1120Area of larger circle = π×82= 64π Area of sector = 72360×area of larger circle = 15×64π = 64π5 Area of smaller circle = π×42 = 16π Probability of event E1, P(point lies inside the sector)=64π564π=15 Probability of event E2, P(point lies inside the smaller circle)=16π64π=14 Let E3 be the event of the point lying neither inside the smaller circle nor inside the sector. Probability of an event E3=1−E1−E2 (Sum of complementary events is 1). P( the point lying neither inside the smaller circle nor inside the sector.) =1−15−14=1120

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